Solve a^2x^2+7ax-8=

$$a ^ { 2 } x ^ { 2 } + 7 a x - 8 =$$

Factor

$$\left(ax-1\right)\left(ax+8\right)$$

Solution Steps

Consider a^{2}x^{2}+7ax-8 as a polynomial over variable a.

$$x^{2}a^{2}+7xa-8$$

Find one factor of the form x^{k}a^{m}+n, where x^{k}a^{m} divides the monomial with the highest power x^{2}a^{2} and n divides the constant factor -8. One such factor is ax+8. Factor the polynomial by dividing it by this factor.

$$\left(ax+8\right)\left(ax-1\right)$$

Evaluate

$$\left(ax-1\right)\left(ax+8\right)$$